Multiplying mechanism



Feb. 5, 1946. MM 2,394,181

MULTIPLYING MECHANISM Filed Oct. 29, 1945 5 Sheets-Sheet 1 5 INVENTOR.

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Feb. 5, 1946. L. w. [MM 2,394,181

MULTIPLYING MECHANISM Filed Oct. 29,1943 5 Shets-Sheet 2 I INVENTOR- Lewzs m 221 A TTORNEY.

Feb. 5, 1 946. w, M 2,394,181

MULTIPLYING MECHANISM Filed 001;. 29, 1943 5 Sheets-Sheet 3 lzb INVENTOR.

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MULTIPLYING MECHANISM Filed Oct. 29, 1945 5 Sheets-Sheet 4 INVENTOR.

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MULTIPLYING MECHANISM 5 Sheets-Sheet 5 Filed Oct. 29, 1943 INVENTOR. Lea/.25 PM 1m 11!.

Patented Feb. 5, 1946 UNITED STATES PATENT OFFICE MULTIPLYING MEClLiNISM Lewis William Imm, Glendale, Calif.

Application October 29, 1943, Serial No. 508,232

1 Claim.

The object of this invention ls to provide a multiplying mechanism operating on the principle that the product of two numberssuch as a and b may be obtained by squaring the sum of the numbers and the difference of the numbers, then subtracting the square of the difference of the numbers from the square of the sum of the numbers giving 4ab and then dividing by 4. In my companion application, Serial No. 508,231, filed October 29, 1943, for a Squaring mechanism, I have disclosed and claimed the combination of a cone, a cylinder, and a cable trained about the cone and cylinder so that part of the cable wound upon the cone forms an Archimedean spiral but in which the cone instead of tapering to a physical point is truncated at a point where its radius is about .2 to .25 of an inch, such truncation being necessary in order to facilitate manufacture of a squaring mechanism operating on the principle disclosed. Due to the truncation of the cone a differential mechanism is employed in a manner disclosed in detail in the aforesaid application to compensate for the truncation of the cone by in effect transferring the zero point of the cone to the plane in. which it is truncated.

The application is a continuation in part of my co-pending application for Squaring mechanism, Serial Number 508,231, filed as of even date herewith.

The invention may be better understood by referring to the attached drawings, in which:

Fig. 1 is a front elevational view of the machine,

Fig. 2 is a front elevational view partly in cross section, of certain of the parts mounted on the back wall and taken on substantially the line 2-2 of Fig. 3,

Fig. 3 is a fragmentary top plan view of the parts mounted on the front wall of the machine,

Fig. 4 is a diagrammatic view of a part of the gearing employed,

Fig. 5 is an elevational view on substantially the line 5-5 of Fig. 2,

Fig. 6 is an exploded view of one of the differential mechanisms,

Fig. 7 is a cross section view of the differential mechanism shown in Fig. 6 and taken on the line 1-1 of Fiz. 8,

Fig. 8 is an elevational view, partly in cross sec- 7 tion, of the differential mechanism shown in Fig. 6 and taken on approximately the line I-8 of Fig. 'l,

Fig. 9 is a view similar to Fig. 7 but taken on the line 9-9 of Fig. 8,

Fig. 10 is an elevational view taken on the line Ill-l0 of Fig. 9,

Fig. 11 is a side elevational view of the spider forming a part of the differential mechanism shown in Fig. 6,

Fig. 12 is a top plan view of the spider shown in Fig. 11,

Fig. 13 is a perspective view of the internal mechanism of the machine looking toward the front wall, certain of the parts being omitted, and

Fig. 14 is an exploded view of a second type of differential mechanism.

The frame of the machine consists of a front wall I, a rear wall 2 and rods 3, spacing and connecting the said walls. Of "course the machine is provided with'a suitable housing, not

shown.

Rotatably mounted in the said walls are input shafts 4a and 4b actuated by knobs 5a and 5b respectively. The shaft 41) has secured thereto a disc 6b, a gear lb and a pinion 8b while the shaft 4a has secured thereto a disc 6a, a gear la and a pinion 8a. The pinion 8b drives a gear 9b secured to shaft lllb to which is secured pinion lib, which drives gear l2b secured to shaft IN), to which is secured disc Mb. The dial or disc 6b is calibrated in suitable scale digits to represent units to be read relative to a reference point l5b, while dial Mb is calibrated in suitable digits to represent a higher scale to be read relative to a reference point lGb.

In like manner the pinion 8a drives gear 9a secured to a shaft Illa, to which is secured pinion lla, which drives gear l2a secured to shaft l3a, to which is secured the higher scale disc Ha, the units disc 6a being read relative to a reference point 15a and the higher scale disc Ila being read relative to a reference point Mia.

The discs 61) and lib simply indicate the value entered by rotating the knob 5b whil the discs 80. and Ila indicate the value entered by rotating the knob 5a.

There are five differential mechanisms which I have indicated in Fig. 4 as I to V inclusive. The gear la drives a gear ll of differential mechanism No. II which type of diiferential mechanism is shown in Fig. 14. The gear ll has secured thereto a pinion lll which drives pinions I9 mounted On arbors 20, carried by arms 2| of a spider 22, which pinions l9 drive pinions 23 carried by arms 24 of the spider. The pinions 23 mesh with the pinion 24 secured to gear 25.

The gears l1 and 25 are free to rotate on shaft 26 while the spider 22 is secured to the said shaft 26.

The gear lb drives the gear 25 to which is secured the pinion 24. The gears l1 and 25 rotate in the same direction when increased values are being set into the mechanism by knobs a and 5b so that the shaft 26 and cone 21 secured thereto rotate an amount corresponding to the sum of a+b.

Differential mechanism No. I is similar to differential mechanism No. II. It will be remembered that knob 5b actuates gear 25. This gear 25 drives gear 21' while gear la drives gear 28 of differential mechanism No. I. These gears are freely mounted on shaft 29 to which is secured the cone 30. These gears form a part of differential mechanism No. I which operates precisely as the differential mechanism shown in Fig. 14, except that obviously in differential mechanism No. II the gears rotate in the same direction when increased values are being added so as to give the sum of a+b while in differential mechanism No. I they will rotate in opposite directions to give a value corresponding to ab.

As heretofore stated, the cones 21 and 30 are secured to shafts 26 and 29 respectively. As shown in Fig. 13 these cones taper in opposite directions, the small end of the cone 2'! being nearest the front wall, while the small end of the cone 3!! is near the rear wall. While I call these cones, each is more precisely a frustum of a cone. These cones act in conjunction with cylinders 3| and 32 respectively,

As fully explained in my co-pending application. Serial Number 508,231, each of these cones is provided with two sets of spiral threads 33 and 34 which receive ribbons or cables 35 and 28 respectively. One of these cables is secured to the small end of its cone such as in Fig. 5, the

.end nearest the front plate, and after leaving the cone is wound around its cylinder and is connected to the end of its cylinder nearest the rear wall. The other cable is secured to the large or rear end of the cone and after leaving the cone is wound around its cylinder and is connected to the front end of its cylinder. These threads form Archimedean spirals.

It is obvious that if the cone tapered to an absolute zero value, an indicator might be actuated to indicate directly the square of the number corresponding to the rotations of the cone. However, it is not practical for the cone to extend to a point. It is, therefore, necessary to provide a differential mechanism to take care of certain complications which arise. This is apparent for if the cone extended to a point and if the cable secured to that point had not yet been wound about the cone, one revolution of the cone would wind very little of that cable on the cylinder and, hence, would rotate the cylinder very slightly. However, with the cable being attached to the cone at its smallest point, one rotation of the cone would now impart far more rotation to the cylinder than if the cone had extended to the zero point.

This differential IV is of the type shown in Fig. 6 in which the cylinder 2| actuated by the cone 2! has secured thereto a pinion 31 which meshes with and drives the piniorrs 28 on a differential spider I8, which also carries pinions 40 meshing with the pinions 28 and which pinions 40 mesh with the pinion 4| secured to a gear 42. The gear 43 is secured to the spider 28. The scar 44 (Fig. {4) is secured to the shaft 2| to h I: in

which is also secured the cone 21, and this gear 44 drives the gear 42. It, therefore, appears thai the spider and gear 43 are actuated both by the rotations of cylinder II from the squaring mechanism as well as by the gear 42.

As above stated, if the cone would extend to a zero value, and if the value entered on the cone as above described were a+b, obviously the cylinder would be rotated in the amount corresponding to a+2ab+b', or if the cone were rotated in an amount corresponding to (1-42, the cylinder would rotate in an amount corresponding to a2ab+b. However, with the radius of the cone at its smallest point having a value of c, we are in effect not squaring a+b, but are squaring a+b+c, obtaining a'-+2ab+b+2c(0+b)+c. Therefore, mechanisms must be provided to eliminate the 2c(a+b) +0 This is done as follows:

The 2c(a+b) is eliminated by differential No. IV while the value of c is subtracted by the gear setting from the output of differentials IV to V.

The diameter of the small end of the cone 21 is to the diameter of the cylinder 3| as the gear 44 secured to the shaft 26 is to the gear 42. If the gear 25 is to the gear 42 as 1% is to 3 as indicated in Fig.4, and if the diameter of the cylinder 3| is one inch, the diameter of the small end of the cone 2'! would be .416667 inch. Since these numbers are somewhat involved, the operation of this differential No. IV might be more easily explained if, for the purpose of illustration, we consider that the radius of the cone at its smallest point is .25 inch, the diameter of the cylinder is one inch and the gear ratio between the gears 25 and 42 is as 1 is to 2. Furthermore, the operation might be further simplified to show how the 2c(a+b) is eliminated by differential No. IV if we allow a+'b to equal 1: so that the expression a+b+c becomes :c+c and the square of this number equals :r+2:cc+c', a: being the number to be squared and 0 being the radius of the cone at the smallest point or, in the il1ustration given above, .25 inch. It will be noted that there is a relationship between :1: and c, for if the cone increases in radius .01 inch for each rotation, .1: would be equal to the radius of the cone at its smallest point 0 plus the number of revolutions which the cone rotates multiplied by its increase in radius per rotation. Assuming that 1: equals any number which we desire to square such as 5, then the radius of the cone at the take-off point would be .3". We would now have fed enough wire from the cone to the cylinder to rotate the cylinder and the pinion 21 2.75 times. The gear 42 would now have rotated in the opposite direction from the pinion 31 2 /2 revolutions if the gear ratio in the hypothetical example given were 1 to 2. The net result would be that the gear 42 would have rotated /2 of the difference between the rotations of the gear 42 and pinion 31, or of a revolution. Obviously this amount of rotation is proportional to the number 5 being squared, and it might be directly indicated if the gear 42 drove another gear of /2 its size so that its shaft would have rotated A of a revolution. If now an indicator were connected with this last gear and had calibrations reading from 0 to 100, the reading given by the dial would be X.25 or 25. which is the square of the number 5. In the above example the c squared would be .0625 and, of course, this number could be eliminated by the gear setting of the output of differential IV into the differential V. In practice, howeven-ifih? gear 4: drives a gear 4| of differential No. V and these gear ratios be either positive or negative depending upon whether or not a is greater than b. The zero position of the cone 21 is therefore its smallest point while the zero position of the cone III is its mid-portion.

It will be remembered that the differential No. I which is the a-b differential is driven from the knobs Ia and b, the gear 1a entering the value a through the gear 28 while the value minus b is entered through the gears lb, 25 and 21'. A gear 46 is secured to the cone shaft 29 and this gear meshes with and drives the gear 41 of differential mechanism N0. III. This mechanism is the same type of mechanism as shown in Fig. 6 so that the gear 41 is the same type gear as the gear 42 and carries a pinion identicalto the pinion 4|. The cylinder I2 carries a pinion identical to pinion 31 and drives a spider identical to spider 39 to which is secured a gear equal 400 units in terms of (H-b). The same is true of gear 4! rotating in the opposite direction in terms of (a-b) The differential spider moves it of the amount of rotation of either input and in the same direction as the movement of the input. Therefore, the calibration of the spider shaft 5i would be 800 units in terms of (a+b)'-(a-b)*.. This, however, is 4ab. The calibrations on the dial attached to the shaft II would be 800 divided by 4 or 200 units per revolution in terms of ab. The /4 revolution would, therefore, equal 50 units or theproduct of axb in the illustration used when (1 equals 10 and b equals 5.

The output shaft II has secured thereto a units dial II to be read relative to a reference line 53. A tens dial 54 is also provided to be read relative to a reference line I! which tens dial is on a shaft 56. The shaft II is provided with a pinion 61 which drives gear 5| secured to shaft 59. to which is secured gear which drives a gear II on shaft II.

It is, therefore, apparent that the above described mechanism will multiply any two numbers 4' which corresponds to the gear 43 of Fig. 6.

Differential No. III, therefore, eliminates 2c(ab) in precisely the same manner as differential No. IVeliminated 2c(a+b).

The gear 48 of differential No. III meshes with and drives gear 49 of differential No. V. The gear setting between these gears subtracts the value c.

It is. therefore, apparent that gear 48 actuates differential No. V by an amount a +2ab+b while the gear 48 enters a value into differential No. V of a*2ab+b.

The differential No. 'V is of the same type as the differential shown in Fig. 14 so that the gear 48 corresponds to the gear 25 and the gear 49 corresponds to the gear l'l, while the spider, corresponding to spider 22, is secured to output shaft II. The function of this differential mechanism No. V might be better understood by giving a speciflcillustration as to its operation. If the input knobs for a and b are at zero, then the output shaft 5| would be at its zero position. Suppose we increase a from 0 to 10. leaving b at zero. The gear 48 would, during this operation, rotate anti-clockwise V4 of a revolution while the gear 4! would have rotated clockwise V4 of a revolution so that the output shaft ll remains stationary. If we now entered a value 'for b of 5,.the gear 49 would move clockwise 1' of a revolution while the gear 45 would rotate clockwise '1'; of a revolution so that the gear 4! is of a revolution anti-clockwise from its zero point, and the gear 45 is 1" of a revolution clockwise from its zero point with: the netresult that the output shaft 5| has rotated clockwise by t;

of the difference between 1'; and 1% orin other words, it would have rotated /4 of a revolution clockwise. The-gear 43 rotatedthe gear, Y4 of a revolution for. 100 units in terms of, (a +b)'.

Therefore one of the revolutionsof gear 4! would such as a and b and irrespective of the fact of whether a is larger or smaller than D.

While I have shown the multiplying mechanism as provided with manually operated input knobs and with scales representing the output, I fully realize that one of the principal utilities of this invention would be as a part of a larger machine which requires direct multiplication as one 01 the functions thereof. In practice, therefore, the inputs instead of being knobs, would probably be operated from other mechanism of a more complicated machine, and the output might be a direct reading indicator or it might be the input to some other part of the machine of which it formed a part.

I realize that many changes may be made in the specific form of the invention as shown by way of. illustration herein. I. therefore, desire to claim the same broadly except as I might limit myself in the following claim.

Having now described my invention I claim:

In a multiplying mechanism, a pair of squaring mechanisms each comprising an input cone element. an output cylinder element, a cable wound on both said cone and said cylinder, and a differential mechanism disposed coaxially with each of said cylinder elements and having an operating connection therewith. all of said elements being mounted on parallel shafts supported by a pair or frame plates; means for adding two variable numbers comprising a third differential mechanism coaxial with the cone element of one of said squaring mechanisms and having an operating connection therewith, means for subtracting one of said variable numbers from the other comprising a fourth differential mechanism coaxial with the cone element of the other of said squaring m and having an opcrating connection therewith, and a further differential mechanism mounted on an additional parallel shaft and controlled jointly by said .first two differentiai mechanisms for subtracting the square of the difference of said numbers from the square of the sum of said numbers. 

